Well, I believe its cutoff is near 2.5V, and as others have seen, it tends to go "pulsed" when it reaches the threshold voltage (its really just turning off as the battery voltage dips below voltage and back on as the voltage rises back up after the load is disconnected). That is probably what is going on. These aren't like mine where the power gradually decreases as the battery voltage drops below the "dropout voltage", these are either ON or OFF.
I'm assuming that you guys are measuring your batteries when the laser is not on (ie, no load)? Because, when a load is put onto a battery, the voltage will dip... depending on how much "juice" is left in the battery, that dip can be huge. So, what's probably happening is that with no load, the batteries voltages are fine, but as soon as you turn on the laser, that load causes the voltage to drop very close to the threshold for the lavadrive.